Curious what I need to drywall around the 2x4 that is extending out of the ceiling in the photo. There used to be a wall where the 2x4 is, but we are joining the two rooms that were previously separated by the wall. Since the 2x4 is not flush with the ceiling, I'm wondering what is the proper way to drywall over that piece of wood.
If the removed wall wasn't structural, you should be able to remove the 2x4 and replace it with something thinner (like the same 2x4 run through a planer) to make it flush with the rest of the ceiling, then install a long, narrow piece of drywall to bring it flush with the existing ceiling.
If the rest of the ceiling has 5/8" drywall (for strength hanging flat on the ceiling) you could get away with 1/2" drywall for this piece (or whatever thickness you're using on the walls) since it would be almost 100% supported by the wood behind it. Just adjust the thickness of the replacement piece to match up with the thickness of drywall you're using.
You have two good options.
1 - Either frame around it with full soffits with 2x2 and drywall on top, or wood to make it look like beams (usually would add a few more "beams" at regular intervals so it looks intentional.
2 - You can lower the drywall around it by removing the whole ceiling, add furring strips to lower the level to match the beam, and drywall the whole ceiling at the lower level.
Other (bad) options would include 1 - Inclined drywall on both sides so that it meets the level of the beam - this would be very hard to do well over short ceiling spans and is likely to look terrible.
2 - You could replace that beam with something shorter - usually wall replacements with steel beams or engineered joists are done to keep the ceilings flat, but this isn't easy or fast and often requires structural engineer analysis (which is expensive) so that's why I put it in the "bad option" category - what you have should work fine.